Calculate the cost of both options

Question

josh needs $320 to pay off his cell phone. He can use his credit card, but the $320 payment will put him at his card limit. His other option is to take a payday loan. His credit card has an annual rate of 16.8% compounded daily. The payday loan charges a daily rate of 0.75%. Calculate the cost of both options if he will pay both off when he receives his next pay cheque in 3 weeks.

awnsers: 

Cost pay day loan: I=$50.40

Cost of credit card: I=$3.11

 

I don't how to find the awnser.

Answer 1

Note that 3 weeks = 21 days 

 

The payday loan charges 0.75% per day for 21 days = 0.75% * 21 = 15.75% total 

15.75% of 320 is 0.1575*320 = $50.40 

 

For the credit card you need to use the formula for compound interest which is 

 

A = P*(1 + r/n)^n*t   where 

 

A = Accumulated or final amount 

P = Principal or original amount (320 in this case)

r = interest rate as a decimal (0.168 in this case)

n = number of compoundings per year (365 in this case)

t = time in years (21/365 in this case) 

 

A = 320*(1 + 0.168/365)^365*(21/365) 

A = 320*(1 + 0.000460274)²¹ 

A = 320*(1.000460274)²¹

A = 320*1.00971

A = 323.1072 = 323.11 to the nearest cent 

 

This amount includes both principal and interest, so the interest cost is 

323.11 - 320 = $3.11